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**Solving Absolute Value Inequalities**

Algebra 2 Unit 1, Lesson 2.3

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**Solving Absolute Value Inequalities**

Algebraically Graphically

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Solve Algebraically

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**Solve Algebraically 4−𝑥 +15>21**

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**Solve on your own: 𝑥+1 −10≤−2**

Remember to isolate absolute value Separate into two equations and reverse.

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**Solution 4−𝑥 +15≥21 −12≤𝑥 𝑎𝑛𝑑 𝑥≤4 −12≤𝑥≤4**

−12≤𝑥 𝑎𝑛𝑑 𝑥≤ −12≤𝑥≤4 Why is the format of the solution different?

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Practice Pause and solve problems 11, 12, and 13 from lesson 3 in your assignment packet. 11. 2 𝑥− >4 𝑥+1 −4<5 𝑥+4 +2≥5

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**Practice Solutions 11. 𝑥<3 𝑜𝑟 𝑥>4**

12. −5<𝑥 𝑎𝑛𝑑 𝑥< −5<𝑥<4 13. 𝑥≤−5 𝑜𝑟 𝑥≥−3 𝑥<3 𝑜𝑟 𝑥>4

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**Solving Graphically 𝑥+3 +1>4**

Solve the inequality graphically Graph both sides of the equation y= 𝑥+3 +1 𝑦=4

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**Solving Graphically 𝑥+3 +1>4**

Solve the inequality graphically Graph both sides of the equation y= 𝑥+3 +1 𝑦=4 Intervals on the x axis: −6≥𝑥 𝑜𝑟 𝑥≥0

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On your Own Solve: 𝑥 −2 −3≤1 Hint: Begin by graphing both sides

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**On your Own Solve: 𝑥 −2 −3≤1 Final Solution −2≤𝑥≤6**

Hint: Begin by graphing both sides Final Solution −2≤𝑥≤6 Why different format?

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Final Thoughts When does an absolute value inequality apply to a real-world situation? Remember you can always check your solution but placing a value in for the variable to see if the equation remains true.

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